LMFDB - Embedded newform 1040.2.da.b.881.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1040,2,Mod(641,1040)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1040, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1040.641");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1040 = 2^{4} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1040.da (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.30444181021$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.22581504.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 $ x^8 - 4x^7 + 5x^6 + 2x^5 - 11x^4 + 4x^3 + 20x^2 - 32*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			881.1
Root			$1.20036 + 0.747754i$ of defining polynomial
Character	$\chi$	$=$	1040.881
Dual form			1040.2.da.b.641.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41342 - 2.44811i) q^{3} +1.00000i q^{5} +(1.64996 + 0.952606i) q^{7} +(-2.49551 + 4.32235i) q^{9} +O(q^{10})$	\(q+(-1.41342 - 2.44811i) q^{3} +1.00000i q^{5} +(1.64996 + 0.952606i) q^{7} +(-2.49551 + 4.32235i) q^{9} +(-0.926118 + 0.534695i) q^{11} +(1.40072 - 3.32235i) q^{13} +(2.44811 - 1.41342i) q^{15} +(0.318632 - 0.551886i) q^{17} +(-4.96410 - 2.86603i) q^{19} -5.38573i q^{21} +(-1.90893 - 3.30636i) q^{23} -1.00000 q^{25} +5.62828 q^{27} +(-4.72756 - 8.18837i) q^{29} -1.46410i q^{31} +(2.61799 + 1.51150i) q^{33} +(-0.952606 + 1.64996i) q^{35} +(0.655970 - 0.378725i) q^{37} +(-10.1133 + 1.26675i) q^{39} +(-0.232051 + 0.133975i) q^{41} +(-0.318632 + 0.551886i) q^{43} +(-4.32235 - 2.49551i) q^{45} +9.44613i q^{47} +(-1.68508 - 2.91865i) q^{49} -1.80144 q^{51} -6.99102 q^{53} +(-0.534695 - 0.926118i) q^{55} +16.2036i q^{57} +(0.641756 + 0.370518i) q^{59} +(-2.09928 + 3.63606i) q^{61} +(-8.23499 + 4.75447i) q^{63} +(3.32235 + 1.40072i) q^{65} +(7.01029 - 4.04739i) q^{67} +(-5.39623 + 9.34654i) q^{69} +(-8.45663 - 4.88244i) q^{71} -3.71649i q^{73} +(1.41342 + 2.44811i) q^{75} -2.03741 q^{77} +9.31937 q^{79} +(-0.468594 - 0.811629i) q^{81} +5.11778i q^{83} +(0.551886 + 0.318632i) q^{85} +(-13.3640 + 23.1472i) q^{87} +(-10.8932 + 6.28917i) q^{89} +(5.47602 - 4.14741i) q^{91} +(-3.58429 + 2.06939i) q^{93} +(2.86603 - 4.96410i) q^{95} +(-3.65597 - 2.11078i) q^{97} -5.33734i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} + 6 q^{7} - 4 q^{9}+O(q^{10}) $ 8 * q - 2 * q^3 + 6 * q^7 - 4 * q^9	$ 8 q - 2 q^{3} + 6 q^{7} - 4 q^{9} + 6 q^{15} - 2 q^{17} - 12 q^{19} + 10 q^{23} - 8 q^{25} + 4 q^{27} - 8 q^{29} + 42 q^{33} - 10 q^{35} + 6 q^{37} + 12 q^{41} + 2 q^{43} + 12 q^{49} + 8 q^{51} - 24 q^{53} + 12 q^{59} - 28 q^{61} + 24 q^{63} - 8 q^{65} - 6 q^{67} - 16 q^{69} + 2 q^{75} - 36 q^{77} + 16 q^{79} + 8 q^{81} + 18 q^{85} - 22 q^{87} + 24 q^{89} - 28 q^{91} + 16 q^{95} - 30 q^{97}+O(q^{100}) $ 8 * q - 2 * q^3 + 6 * q^7 - 4 * q^9 + 6 * q^15 - 2 * q^17 - 12 * q^19 + 10 * q^23 - 8 * q^25 + 4 * q^27 - 8 * q^29 + 42 * q^33 - 10 * q^35 + 6 * q^37 + 12 * q^41 + 2 * q^43 + 12 * q^49 + 8 * q^51 - 24 * q^53 + 12 * q^59 - 28 * q^61 + 24 * q^63 - 8 * q^65 - 6 * q^67 - 16 * q^69 + 2 * q^75 - 36 * q^77 + 16 * q^79 + 8 * q^81 + 18 * q^85 - 22 * q^87 + 24 * q^89 - 28 * q^91 + 16 * q^95 - 30 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times$.

$n$	$261$	$417$	$561$	$911$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.41342	−	2.44811i	−0.816038	−	1.41342i	−0.908580	−	0.417710i	$-0.862833\pi$
$3$	−1.41342	−	2.44811i	−0.816038	−	1.41342i	0.0925423	−	0.995709i	$-0.470501\pi$
$4$		0			0
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$		0			0
$7$	1.64996	+	0.952606i	0.623627	+	0.360051i	0.778280	−	0.627918i	$-0.216093\pi$
$7$	1.64996	+	0.952606i	0.623627	+	0.360051i	−0.154653	+	0.987969i	$0.549426\pi$
$8$		0			0
$9$	−2.49551	+	4.32235i	−0.831836	+	1.44078i
$10$		0			0
$11$	−0.926118	+	0.534695i	−0.279235	+	0.161217i	−0.633077	−	0.774089i	$-0.718208\pi$
$11$	−0.926118	+	0.534695i	−0.279235	+	0.161217i	0.353842	+	0.935305i	$0.384875\pi$
$12$		0			0
$13$	1.40072	−	3.32235i	0.388490	−	0.921453i
$13$	1.40072	−	3.32235i	0.388490	−	0.921453i
$14$		0			0
$15$	2.44811	−	1.41342i	0.632100	−	0.364943i
$16$		0			0
$17$	0.318632	−	0.551886i	0.0772795	−	0.133852i	−0.824796	−	0.565431i	$-0.808710\pi$
$17$	0.318632	−	0.551886i	0.0772795	−	0.133852i	0.902075	+	0.431579i	$0.142043\pi$
$18$		0			0
$19$	−4.96410	−	2.86603i	−1.13884	−	0.657511i	−0.192699	−	0.981258i	$-0.561724\pi$
$19$	−4.96410	−	2.86603i	−1.13884	−	0.657511i	−0.946144	+	0.323747i	$0.895057\pi$
$20$		0			0
$21$		−	5.38573i		−	1.17526i
$22$		0			0
$23$	−1.90893	−	3.30636i	−0.398039	−	0.689423i	0.595445	−	0.803396i	$-0.296976\pi$
$23$	−1.90893	−	3.30636i	−0.398039	−	0.689423i	−0.993484	+	0.113973i	$0.963642\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$		0			0
$27$	5.62828			1.08316
$28$		0			0
$29$	−4.72756	−	8.18837i	−0.877886	−	1.52054i	−0.853657	−	0.520836i	$-0.825620\pi$
$29$	−4.72756	−	8.18837i	−0.877886	−	1.52054i	−0.0242288	−	0.999706i	$-0.507713\pi$
$30$		0			0
$31$		−	1.46410i		−	0.262960i	−0.991319	−	0.131480i	$-0.958027\pi$
$31$		−	1.46410i		−	0.262960i	0.991319	−	0.131480i	$-0.0419730\pi$
$32$		0			0
$33$	2.61799	+	1.51150i	0.455733	+	0.263118i
$34$		0			0
$35$	−0.952606	+	1.64996i	−0.161020	+	0.278895i
$36$		0			0
$37$	0.655970	−	0.378725i	0.107841	−	0.0622619i	−0.445110	−	0.895476i	$-0.646835\pi$
$37$	0.655970	−	0.378725i	0.107841	−	0.0622619i	0.552950	+	0.833214i	$0.313502\pi$
$38$		0			0
$39$	−10.1133	+	1.26675i	−1.61942	+	0.202842i
$40$		0			0
$41$	−0.232051	+	0.133975i	−0.0362402	+	0.0209233i	−0.518011	−	0.855374i	$-0.673327\pi$
$41$	−0.232051	+	0.133975i	−0.0362402	+	0.0209233i	0.481770	+	0.876297i	$0.339994\pi$
$42$		0			0
$43$	−0.318632	+	0.551886i	−0.0485909	+	0.0841618i	−0.889298	−	0.457328i	$-0.848806\pi$
$43$	−0.318632	+	0.551886i	−0.0485909	+	0.0841618i	0.840707	+	0.541490i	$0.182140\pi$
$44$		0			0
$45$	−4.32235	−	2.49551i	−0.644337	−	0.372008i
$46$		0			0
$47$			9.44613i			1.37786i	0.724828	+	0.688930i	$0.241919\pi$
$47$			9.44613i			1.37786i	−0.724828	+	0.688930i	$0.758081\pi$
$48$		0			0
$49$	−1.68508	−	2.91865i	−0.240726	−	0.416950i
$50$		0			0
$51$	−1.80144			−0.252252
$52$		0			0
$53$	−6.99102			−0.960290			−0.480145	−	0.877189i	$-0.659416\pi$
$53$	−6.99102			−0.960290			−0.480145	+	0.877189i	$0.659416\pi$
$54$		0			0
$55$	−0.534695	−	0.926118i	−0.0720982	−	0.124878i
$56$		0			0
$57$			16.2036i			2.14622i
$58$		0			0
$59$	0.641756	+	0.370518i	0.0835495	+	0.0482373i	0.541193	−	0.840899i	$-0.317973\pi$
$59$	0.641756	+	0.370518i	0.0835495	+	0.0482373i	−0.457643	+	0.889136i	$0.651306\pi$
$60$		0			0
$61$	−2.09928	+	3.63606i	−0.268785	+	0.465550i	−0.968548	−	0.248825i	$-0.919956\pi$
$61$	−2.09928	+	3.63606i	−0.268785	+	0.465550i	0.699763	+	0.714375i	$0.253289\pi$
$62$		0			0
$63$	−8.23499	+	4.75447i	−1.03751	+	0.599007i
$64$		0			0
$65$	3.32235	+	1.40072i	0.412086	+	0.173738i
$66$		0			0
$67$	7.01029	−	4.04739i	0.856443	−	0.494468i	−0.00637624	−	0.999980i	$-0.502030\pi$
$67$	7.01029	−	4.04739i	0.856443	−	0.494468i	0.862820	+	0.505512i	$0.168696\pi$
$68$		0			0
$69$	−5.39623	+	9.34654i	−0.649629	+	1.12519i
$70$		0			0
$71$	−8.45663	−	4.88244i	−1.00362	−	0.579439i	−0.0943010	−	0.995544i	$-0.530062\pi$
$71$	−8.45663	−	4.88244i	−1.00362	−	0.579439i	−0.909317	+	0.416105i	$0.863395\pi$
$72$		0			0
$73$		−	3.71649i		−	0.434982i	−0.976062	−	0.217491i	$-0.930213\pi$
$73$		−	3.71649i		−	0.434982i	0.976062	−	0.217491i	$-0.0697873\pi$
$74$		0			0
$75$	1.41342	+	2.44811i	0.163208	+	0.282684i
$76$		0			0
$77$	−2.03741			−0.232185
$78$		0			0
$79$	9.31937			1.04851			0.524255	−	0.851561i	$-0.324344\pi$
$79$	9.31937			1.04851			0.524255	+	0.851561i	$0.324344\pi$
$80$		0			0
$81$	−0.468594	−	0.811629i	−0.0520660	−	0.0901809i
$82$		0			0
$83$			5.11778i			0.561749i	0.959744	+	0.280875i	$0.0906245\pi$
$83$			5.11778i			0.561749i	−0.959744	+	0.280875i	$0.909376\pi$
$84$		0			0
$85$	0.551886	+	0.318632i	0.0598605	+	0.0345605i
$86$		0			0
$87$	−13.3640	+	23.1472i	−1.43278	+	2.48164i
$88$		0			0
$89$	−10.8932	+	6.28917i	−1.15467	+	0.666650i	−0.950021	−	0.312185i	$-0.898939\pi$
$89$	−10.8932	+	6.28917i	−1.15467	+	0.666650i	−0.204651	+	0.978835i	$0.565606\pi$
$90$		0			0
$91$	5.47602	−	4.14741i	0.574043	−	0.434767i
$92$		0			0
$93$	−3.58429	+	2.06939i	−0.371673	+	0.214586i
$94$		0			0
$95$	2.86603	−	4.96410i	0.294048	−	0.509306i
$96$		0			0
$97$	−3.65597	−	2.11078i	−0.371208	−	0.214317i	0.302778	−	0.953061i	$-0.402086\pi$
$97$	−3.65597	−	2.11078i	−0.371208	−	0.214317i	−0.673986	+	0.738744i	$0.735419\pi$
$98$		0			0
$99$		−	5.33734i		−	0.536423i
$100$		0			0
$101$	−7.62379	−	13.2048i	−0.758595	−	1.31393i	−0.943567	−	0.331181i	$-0.892553\pi$
$101$	−7.62379	−	13.2048i	−0.758595	−	1.31393i	0.184972	−	0.982744i	$-0.440781\pi$
$102$		0			0
$103$	−13.5269			−1.33285			−0.666423	−	0.745574i	$-0.732176\pi$
$103$	−13.5269			−1.33285			−0.666423	+	0.745574i	$0.732176\pi$
$104$		0			0
$105$	5.38573			0.525593
$106$		0			0
$107$	−3.68137	−	6.37632i	−0.355891	−	0.616422i	0.631379	−	0.775475i	$-0.282489\pi$
$107$	−3.68137	−	6.37632i	−0.355891	−	0.616422i	−0.987270	+	0.159053i	$0.949156\pi$
$108$		0			0
$109$		−	10.0760i		−	0.965103i	−0.875868	−	0.482551i	$-0.839710\pi$
$109$		−	10.0760i		−	0.965103i	0.875868	−	0.482551i	$-0.160290\pi$
$110$		0			0
$111$	−1.85432	−	1.07059i	−0.176004	−	0.101616i
$112$		0			0
$113$	3.34403	−	5.79203i	0.314580	−	0.544868i	−0.664768	−	0.747050i	$-0.731470\pi$
$113$	3.34403	−	5.79203i	0.314580	−	0.544868i	0.979348	+	0.202181i	$0.0648030\pi$
$114$		0			0
$115$	3.30636	−	1.90893i	0.308320	−	0.178008i
$116$		0			0
$117$	10.8648	+	14.3453i	1.00445	+	1.32623i
$118$		0			0
$119$	1.05146	−	0.607061i	0.0963872	−	0.0556492i
$120$		0			0
$121$	−4.92820	+	8.53590i	−0.448018	+	0.775991i
$122$		0			0
$123$	0.655970	+	0.378725i	0.0591468	+	0.0341484i
$124$		0			0
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$	−0.744750	−	1.28994i	−0.0660859	−	0.114464i	0.831089	−	0.556139i	$-0.187718\pi$
$127$	−0.744750	−	1.28994i	−0.0660859	−	0.114464i	−0.897175	+	0.441675i	$0.854384\pi$
$128$		0			0
$129$	1.80144			0.158608
$130$		0			0
$131$	−4.12676			−0.360557			−0.180278	−	0.983616i	$-0.557700\pi$
$131$	−4.12676			−0.360557			−0.180278	+	0.983616i	$0.557700\pi$
$132$		0			0
$133$	−5.46039	−	9.45767i	−0.473476	−	0.820084i
$134$		0			0
$135$			5.62828i			0.484405i
$136$		0			0
$137$	17.4155	+	10.0548i	1.48790	+	0.859041i	0.999905	−	0.0138029i	$-0.00439372\pi$
$137$	17.4155	+	10.0548i	1.48790	+	0.859041i	0.487999	+	0.872844i	$0.337727\pi$
$138$		0			0
$139$	10.4126	−	18.0352i	0.883189	−	1.52973i	0.0354130	−	0.999373i	$-0.488725\pi$
$139$	10.4126	−	18.0352i	0.883189	−	1.52973i	0.847776	−	0.530355i	$-0.177941\pi$
$140$		0			0
$141$	23.1252	−	13.3513i	1.94749	−	1.12439i
$142$		0			0
$143$	0.479208	+	3.82584i	0.0400734	+	0.319933i
$144$		0			0
$145$	8.18837	−	4.72756i	0.680007	−	0.392602i
$146$		0			0
$147$	−4.76346	+	8.25055i	−0.392883	+	0.680494i
$148$		0			0
$149$	11.5768	+	6.68388i	0.948410	+	0.547565i	0.892587	−	0.450876i	$-0.148888\pi$
$149$	11.5768	+	6.68388i	0.948410	+	0.547565i	0.0558233	+	0.998441i	$0.482222\pi$
$150$		0			0
$151$		−	18.2984i		−	1.48910i	−0.667567	−	0.744550i	$-0.732664\pi$
$151$		−	18.2984i		−	1.48910i	0.667567	−	0.744550i	$-0.267336\pi$
$152$		0			0
$153$	1.59030	+	2.75447i	0.128568	+	0.222686i
$154$		0			0
$155$	1.46410			0.117599
$156$		0			0
$157$	2.42229			0.193320			0.0966599	−	0.995317i	$-0.469184\pi$
$157$	2.42229			0.193320			0.0966599	+	0.995317i	$0.469184\pi$
$158$		0			0
$159$	9.88124	+	17.1148i	0.783633	+	1.35729i
$160$		0			0
$161$		−	7.27382i		−	0.573258i
$162$		0			0
$163$	13.8416	+	7.99144i	1.08416	+	0.625938i	0.932015	−	0.362421i	$-0.118050\pi$
$163$	13.8416	+	7.99144i	1.08416	+	0.625938i	0.152142	+	0.988359i	$0.451383\pi$
$164$		0			0
$165$	−1.51150	+	2.61799i	−0.117670	+	0.203810i
$166$		0			0
$167$	12.4648	−	7.19658i	0.964558	−	0.556888i	0.0669853	−	0.997754i	$-0.478662\pi$
$167$	12.4648	−	7.19658i	0.964558	−	0.556888i	0.897573	+	0.440866i	$0.145329\pi$
$168$		0			0
$169$	−9.07597	−	9.30735i	−0.698151	−	0.715950i
$170$		0			0
$171$	24.7759	−	14.3044i	1.89466	−	1.09388i
$172$		0			0
$173$	−12.1745	+	21.0868i	−0.925608	+	1.60320i	−0.135027	+	0.990842i	$0.543112\pi$
$173$	−12.1745	+	21.0868i	−0.925608	+	1.60320i	−0.790581	+	0.612358i	$0.790221\pi$
$174$		0			0
$175$	−1.64996	−	0.952606i	−0.124725	−	0.0720103i
$176$		0			0
$177$		−	2.09479i		−	0.157454i
$178$		0			0
$179$	−1.89414	−	3.28075i	−0.141575	−	0.245215i	0.786515	−	0.617571i	$-0.211883\pi$
$179$	−1.89414	−	3.28075i	−0.141575	−	0.245215i	−0.928090	+	0.372356i	$0.878550\pi$
$180$		0			0
$181$	8.48794			0.630904			0.315452	−	0.948942i	$-0.397844\pi$
$181$	8.48794			0.630904			0.315452	+	0.948942i	$0.397844\pi$
$182$		0			0
$183$	11.8687			0.877356
$184$		0			0
$185$	0.378725	+	0.655970i	0.0278444	+	0.0482279i
$186$		0			0
$187$			0.681482i			0.0498349i
$188$		0			0
$189$	9.28645	+	5.36153i	0.675490	+	0.389994i
$190$		0			0
$191$	−2.72155	+	4.71386i	−0.196924	+	0.341083i	−0.947530	−	0.319668i	$-0.896429\pi$
$191$	−2.72155	+	4.71386i	−0.196924	+	0.341083i	0.750605	+	0.660751i	$0.229762\pi$
$192$		0			0
$193$	10.5288	−	6.07880i	0.757879	−	0.437562i	−0.0706548	−	0.997501i	$-0.522509\pi$
$193$	10.5288	−	6.07880i	0.757879	−	0.437562i	0.828534	+	0.559939i	$0.189176\pi$
$194$		0			0
$195$	−1.26675	−	10.1133i	−0.0907135	−	0.724227i
$196$		0			0
$197$	3.79172	−	2.18915i	0.270149	−	0.155970i	−0.358807	−	0.933412i	$-0.616816\pi$
$197$	3.79172	−	2.18915i	0.270149	−	0.155970i	0.628955	+	0.777442i	$0.283483\pi$
$198$		0			0
$199$	−10.4186	+	18.0456i	−0.738558	+	1.27922i	0.214586	+	0.976705i	$0.431160\pi$
$199$	−10.4186	+	18.0456i	−0.738558	+	1.27922i	−0.953144	+	0.302516i	$0.902174\pi$
$200$		0			0
$201$	−19.8170	−	11.4413i	−1.39778	−	0.807009i
$202$		0			0
$203$		−	18.0140i		−	1.26434i
$204$		0			0
$205$	−0.133975	−	0.232051i	−0.00935719	−	0.0162071i
$206$		0			0
$207$	19.0550			1.32441
$208$		0			0
$209$	6.12979			0.424007
$210$		0			0
$211$	−5.32684	−	9.22635i	−0.366715	−	0.635168i	0.622335	−	0.782751i	$-0.286184\pi$
$211$	−5.32684	−	9.22635i	−0.366715	−	0.635168i	−0.989050	+	0.147583i	$0.952851\pi$
$212$		0			0
$213$			27.6037i			1.89138i
$214$		0			0
$215$	−0.551886	−	0.318632i	−0.0376383	−	0.0217305i
$216$		0			0
$217$	1.39471	−	2.41571i	0.0946792	−	0.163989i
$218$		0			0
$219$	−9.09839	+	5.25296i	−0.614812	+	0.354962i
$220$		0			0
$221$	−1.38724	−	1.83164i	−0.0933161	−	0.123210i
$222$		0			0
$223$	18.4804	−	10.6697i	1.23754	−	0.714494i	0.268949	−	0.963155i	$-0.413324\pi$
$223$	18.4804	−	10.6697i	1.23754	−	0.714494i	0.968591	+	0.248661i	$0.0799905\pi$
$224$		0			0
$225$	2.49551	−	4.32235i	0.166367	−	0.288156i
$226$		0			0
$227$	−13.5842	−	7.84283i	−0.901613	−	0.520547i	−0.0238900	−	0.999715i	$-0.507605\pi$
$227$	−13.5842	−	7.84283i	−0.901613	−	0.520547i	−0.877723	+	0.479168i	$0.840938\pi$
$228$		0			0
$229$		−	7.62085i		−	0.503600i	−0.967779	−	0.251800i	$-0.918977\pi$
$229$		−	7.62085i		−	0.503600i	0.967779	−	0.251800i	$-0.0810225\pi$
$230$		0			0
$231$	2.87972	+	4.98782i	0.189472	+	0.328175i
$232$		0			0
$233$	19.0550			1.24833			0.624166	−	0.781292i	$-0.285439\pi$
$233$	19.0550			1.24833			0.624166	+	0.781292i	$0.285439\pi$
$234$		0			0
$235$	−9.44613			−0.616198
$236$		0			0
$237$	−13.1722	−	22.8149i	−0.855625	−	1.48199i
$238$		0			0
$239$			12.7535i			0.824954i	0.910968	+	0.412477i	$0.135336\pi$
$239$			12.7535i			0.824954i	−0.910968	+	0.412477i	$0.864664\pi$
$240$		0			0
$241$	−22.4550	−	12.9644i	−1.44646	−	0.835111i	−0.448187	−	0.893940i	$-0.647930\pi$
$241$	−22.4550	−	12.9644i	−1.44646	−	0.835111i	−0.998268	+	0.0588285i	$0.981263\pi$
$242$		0			0
$243$	7.11778	−	12.3284i	0.456606	−	0.790864i
$244$		0			0
$245$	2.91865	−	1.68508i	0.186466	−	0.107656i
$246$		0			0
$247$	−16.4752	+	12.4780i	−1.04829	+	0.793954i
$248$		0			0
$249$	12.5289	−	7.23357i	0.793987	−	0.458409i
$250$		0			0
$251$	−3.80593	+	6.59207i	−0.240228	+	0.416088i	−0.960779	−	0.277314i	$-0.910556\pi$
$251$	−3.80593	+	6.59207i	−0.240228	+	0.416088i	0.720551	+	0.693402i	$0.243889\pi$
$252$		0			0
$253$	3.53578	+	2.04139i	0.222293	+	0.128341i
$254$		0			0
$255$		−	1.80144i		−	0.112811i
$256$		0			0
$257$	0.167891	+	0.290796i	0.0104728	+	0.0181394i	0.871214	−	0.490903i	$-0.163333\pi$
$257$	0.167891	+	0.290796i	0.0104728	+	0.0181394i	−0.860742	+	0.509042i	$0.830000\pi$
$258$		0			0
$259$	1.44310			0.0896700
$260$		0			0
$261$	47.1906			2.92103
$262$		0			0
$263$	−2.68795	−	4.65566i	−0.165746	−	0.287080i	0.771174	−	0.636624i	$-0.219670\pi$
$263$	−2.68795	−	4.65566i	−0.165746	−	0.287080i	−0.936920	+	0.349544i	$0.886336\pi$
$264$		0			0
$265$		−	6.99102i		−	0.429455i
$266$		0			0
$267$	30.7932	+	17.7785i	1.88451	+	1.08802i
$268$		0			0
$269$	0.655192	−	1.13483i	0.0399478	−	0.0691916i	−0.845360	−	0.534197i	$-0.820614\pi$
$269$	0.655192	−	1.13483i	0.0399478	−	0.0691916i	0.885308	+	0.465005i	$0.153948\pi$
$270$		0			0
$271$	10.0851	−	5.82266i	0.612629	−	0.353701i	−0.161365	−	0.986895i	$-0.551590\pi$
$271$	10.0851	−	5.82266i	0.612629	−	0.353701i	0.773994	+	0.633194i	$0.218256\pi$
$272$		0			0
$273$	−17.8933	−	7.54390i	−1.08295	−	0.456577i
$274$		0			0
$275$	0.926118	−	0.534695i	0.0558470	−	0.0322433i
$276$		0			0
$277$	−10.1581	+	17.5943i	−0.610338	+	1.05714i	0.380845	+	0.924639i	$0.375633\pi$
$277$	−10.1581	+	17.5943i	−0.610338	+	1.05714i	−0.991183	+	0.132498i	$0.957700\pi$
$278$		0			0
$279$	6.32835	+	3.65368i	0.378869	+	0.218740i
$280$		0			0
$281$		−	11.8744i		−	0.708366i	−0.935176	−	0.354183i	$-0.884759\pi$
$281$		−	11.8744i		−	0.708366i	0.935176	−	0.354183i	$-0.115241\pi$
$282$		0			0
$283$	11.3261	+	19.6173i	0.673264	+	1.16613i	0.976973	+	0.213363i	$0.0684418\pi$
$283$	11.3261	+	19.6173i	0.673264	+	1.16613i	−0.303709	+	0.952765i	$0.598225\pi$
$284$		0			0
$285$	−16.2036			−0.959817
$286$		0			0
$287$	−0.510500			−0.0301339
$288$		0			0
$289$	8.29695	+	14.3707i	0.488056	+	0.845337i
$290$		0			0
$291$			11.9336i			0.699562i
$292$		0			0
$293$	−16.1191	−	9.30636i	−0.941687	−	0.543683i	−0.0511983	−	0.998689i	$-0.516304\pi$
$293$	−16.1191	−	9.30636i	−0.941687	−	0.543683i	−0.890489	+	0.455005i	$0.849637\pi$
$294$		0			0
$295$	−0.370518	+	0.641756i	−0.0215724	+	0.0373645i
$296$		0			0
$297$	−5.21245	+	3.00941i	−0.302457	+	0.174624i
$298$		0			0
$299$	−13.6587	+	1.71083i	−0.789905	+	0.0989400i
$300$		0			0
$301$	−1.05146	+	0.607061i	−0.0606052	+	0.0349904i
$302$		0			0
$303$	−21.5512	+	37.3278i	−1.23808	+	2.14443i
$304$		0			0
$305$	−3.63606	−	2.09928i	−0.208200	−	0.120204i
$306$		0			0
$307$		−	3.14776i		−	0.179652i	−0.995957	−	0.0898262i	$-0.971369\pi$
$307$		−	3.14776i		−	0.179652i	0.995957	−	0.0898262i	$-0.0286311\pi$
$308$		0			0
$309$	19.1192	+	33.1154i	1.08765	+	1.88387i
$310$		0			0
$311$	−3.18059			−0.180355			−0.0901774	−	0.995926i	$-0.528743\pi$
$311$	−3.18059			−0.180355			−0.0901774	+	0.995926i	$0.528743\pi$
$312$		0			0
$313$	35.3533			1.99829			0.999144	−	0.0413596i	$-0.0131689\pi$
$313$	35.3533			1.99829			0.999144	+	0.0413596i	$0.0131689\pi$
$314$		0			0
$315$	−4.75447	−	8.23499i	−0.267884	−	0.463989i
$316$		0			0
$317$			13.6357i			0.765858i	0.923778	+	0.382929i	$0.125085\pi$
$317$			13.6357i			0.765858i	−0.923778	+	0.382929i	$0.874915\pi$
$318$		0			0
$319$	8.75656	+	5.05560i	0.490273	+	0.283059i
$320$		0			0
$321$	−10.4066	+	18.0248i	−0.580842	+	1.00605i
$322$		0			0
$323$	−3.16344	+	1.82641i	−0.176018	+	0.101624i
$324$		0			0
$325$	−1.40072	+	3.32235i	−0.0776980	+	0.184291i
$326$		0			0
$327$	−24.6671	+	14.2416i	−1.36409	+	0.787560i
$328$		0			0
$329$	−8.99844	+	15.5858i	−0.496100	+	0.859271i
$330$		0			0
$331$	24.9380	+	14.3980i	1.37072	+	0.791383i	0.991018	−	0.133727i	$-0.0426945\pi$
$331$	24.9380	+	14.3980i	1.37072	+	0.791383i	0.379698	+	0.925110i	$0.376028\pi$
$332$		0			0
$333$			3.78044i			0.207167i
$334$		0			0
$335$	4.04739	+	7.01029i	0.221133	+	0.383013i
$336$		0			0
$337$	−11.7493			−0.640026			−0.320013	−	0.947413i	$-0.603687\pi$
$337$	−11.7493			−0.640026			−0.320013	+	0.947413i	$0.603687\pi$
$338$		0			0
$339$	−18.9061			−1.02684
$340$		0			0
$341$	0.782847	+	1.35593i	0.0423936	+	0.0734278i
$342$		0			0
$343$		−	19.7574i		−	1.06680i
$344$		0			0
$345$	−9.34654	−	5.39623i	−0.503201	−	0.290523i
$346$		0			0
$347$	0.949887	−	1.64525i	0.0509926	−	0.0883218i	−0.839402	−	0.543510i	$-0.817095\pi$
$347$	0.949887	−	1.64525i	0.0509926	−	0.0883218i	0.890395	+	0.455189i	$0.150428\pi$
$348$		0			0
$349$	−8.89329	+	5.13454i	−0.476047	+	0.274846i	−0.718768	−	0.695250i	$-0.755293\pi$
$349$	−8.89329	+	5.13454i	−0.476047	+	0.274846i	0.242721	+	0.970096i	$0.421960\pi$
$350$		0			0
$351$	7.88364	−	18.6991i	0.420798	−	0.998084i
$352$		0			0
$353$	−0.693330	+	0.400294i	−0.0369022	+	0.0213055i	−0.518338	−	0.855176i	$-0.673449\pi$
$353$	−0.693330	+	0.400294i	−0.0369022	+	0.0213055i	0.481435	+	0.876482i	$0.340116\pi$
$354$		0			0
$355$	4.88244	−	8.45663i	0.259133	−	0.448831i
$356$		0			0
$357$	−2.97231	−	1.71606i	−0.157311	−	0.0908237i
$358$		0			0
$359$		−	8.13272i		−	0.429228i	−0.976699	−	0.214614i	$-0.931151\pi$
$359$		−	8.13272i		−	0.429228i	0.976699	−	0.214614i	$-0.0688494\pi$
$360$		0			0
$361$	6.92820	+	12.0000i	0.364642	+	0.631579i
$362$		0			0
$363$	27.8625			1.46240
$364$		0			0
$365$	3.71649			0.194530
$366$		0			0
$367$	−10.2632	−	17.7765i	−0.535737	−	0.927924i	−0.999127	−	0.0417696i	$-0.986700\pi$
$367$	−10.2632	−	17.7765i	−0.535737	−	0.927924i	0.463390	−	0.886154i	$-0.346633\pi$
$368$		0			0
$369$		−	1.33734i		−	0.0696191i
$370$		0			0
$371$	−11.5349	−	6.65968i	−0.598863	−	0.345754i
$372$		0			0
$373$	8.90292	−	15.4203i	0.460976	−	0.798433i	−0.538034	−	0.842923i	$-0.680833\pi$
$373$	8.90292	−	15.4203i	0.460976	−	0.798433i	0.999010	+	0.0444897i	$0.0141662\pi$
$374$		0			0
$375$	−2.44811	+	1.41342i	−0.126420	+	0.0729887i
$376$		0			0
$377$	−33.8266	+	4.23697i	−1.74216	+	0.218215i
$378$		0			0
$379$	1.77150	−	1.02277i	0.0909956	−	0.0525363i	−0.453812	−	0.891098i	$-0.649936\pi$
$379$	1.77150	−	1.02277i	0.0909956	−	0.0525363i	0.544807	+	0.838561i	$0.316603\pi$
$380$		0			0
$381$	−2.10529	+	3.64647i	−0.107857	+	0.186814i
$382$		0			0
$383$	6.84611	+	3.95261i	0.349820	+	0.201969i	0.664606	−	0.747194i	$-0.268599\pi$
$383$	6.84611	+	3.95261i	0.349820	+	0.201969i	−0.314786	+	0.949163i	$0.601933\pi$
$384$		0			0
$385$		−	2.03741i		−	0.103836i
$386$		0			0
$387$	−1.59030	−	2.75447i	−0.0808393	−	0.140018i
$388$		0			0
$389$	9.21171			0.467052			0.233526	−	0.972351i	$-0.424974\pi$
$389$	9.21171			0.467052			0.233526	+	0.972351i	$0.424974\pi$
$390$		0			0
$391$	−2.43298			−0.123041
$392$		0			0
$393$	5.83285	+	10.1028i	0.294228	+	0.509618i
$394$		0			0
$395$			9.31937i			0.468908i
$396$		0			0
$397$	5.50305	+	3.17719i	0.276190	+	0.159458i	0.631697	−	0.775215i	$-0.282359\pi$
$397$	5.50305	+	3.17719i	0.276190	+	0.159458i	−0.355507	+	0.934674i	$0.615692\pi$
$398$		0			0
$399$	−15.4356	+	26.7353i	−0.772748	+	1.33844i
$400$		0			0
$401$	3.61063	−	2.08460i	0.180306	−	0.104100i	−0.407130	−	0.913370i	$-0.633470\pi$
$401$	3.61063	−	2.08460i	0.180306	−	0.104100i	0.587437	+	0.809270i	$0.300137\pi$
$402$		0			0
$403$	−4.86425	−	2.05080i	−0.242306	−	0.102157i
$404$		0			0
$405$	0.811629	−	0.468594i	0.0403301	−	0.0232846i
$406$		0			0
$407$	−0.405004	+	0.701487i	−0.0200753	+	0.0347714i
$408$		0			0
$409$	8.80580	+	5.08403i	0.435419	+	0.251389i	0.701652	−	0.712519i	$-0.252446\pi$
$409$	8.80580	+	5.08403i	0.435419	+	0.251389i	−0.266234	+	0.963909i	$0.585779\pi$
$410$		0			0
$411$		−	56.8467i		−	2.80404i
$412$		0			0
$413$	0.705915	+	1.22268i	0.0347358	+	0.0601642i
$414$		0			0
$415$	−5.11778			−0.251222
$416$		0			0
$417$	−58.8697			−2.88286
$418$		0			0
$419$	14.2954	+	24.7604i	0.698378	+	1.20963i	0.969029	+	0.246948i	$0.0794277\pi$
$419$	14.2954	+	24.7604i	0.698378	+	1.20963i	−0.270651	+	0.962677i	$0.587239\pi$
$420$		0			0
$421$		−	2.01797i		−	0.0983498i	−0.998790	−	0.0491749i	$-0.984341\pi$
$421$		−	2.01797i		−	0.0983498i	0.998790	−	0.0491749i	$-0.0156592\pi$
$422$		0			0
$423$	−40.8295	−	23.5729i	−1.98520	−	1.14615i
$424$		0			0
$425$	−0.318632	+	0.551886i	−0.0154559	+	0.0267704i
$426$		0			0
$427$	−6.92747	+	3.99957i	−0.335244	+	0.193553i
$428$		0			0
$429$	8.68878	−	6.58068i	0.419498	−	0.317718i
$430$		0			0
$431$	−17.8508	+	10.3061i	−0.859842	+	0.496430i	−0.863959	−	0.503562i	$-0.832023\pi$
$431$	−17.8508	+	10.3061i	−0.859842	+	0.496430i	0.00411765	+	0.999992i	$0.498689\pi$
$432$		0			0
$433$	14.7178	−	25.4920i	0.707292	−	1.22507i	−0.258566	−	0.965994i	$-0.583250\pi$
$433$	14.7178	−	25.4920i	0.707292	−	1.22507i	0.965858	−	0.259072i	$-0.0834168\pi$
$434$		0			0
$435$	−23.1472	−	13.3640i	−1.10982	−	0.640757i
$436$		0			0
$437$			21.8841i			1.04686i
$438$		0			0
$439$	−8.47602	−	14.6809i	−0.404538	−	0.700681i	0.589729	−	0.807601i	$-0.299235\pi$
$439$	−8.47602	−	14.6809i	−0.404538	−	0.700681i	−0.994268	+	0.106920i	$0.965901\pi$
$440$		0			0
$441$	16.8205			0.800978
$442$		0			0
$443$	24.1399			1.14692			0.573461	−	0.819233i	$-0.305600\pi$
$443$	24.1399			1.14692			0.573461	+	0.819233i	$0.305600\pi$
$444$		0			0
$445$	−6.28917	−	10.8932i	−0.298135	−	0.516385i
$446$		0			0
$447$		−	37.7885i		−	1.78733i
$448$		0			0
$449$	18.0679	+	10.4315i	0.852676	+	0.492293i	0.861553	−	0.507668i	$-0.169492\pi$
$449$	18.0679	+	10.4315i	0.852676	+	0.492293i	−0.00887706	+	0.999961i	$0.502826\pi$
$450$		0			0
$451$	0.143271	−	0.248153i	0.00674637	−	0.0116851i
$452$		0			0
$453$	−44.7965	+	25.8633i	−2.10472	+	1.21516i
$454$		0			0
$455$	4.14741	+	5.47602i	0.194434	+	0.256720i
$456$		0			0
$457$	26.4708	−	15.2830i	1.23825	−	0.714906i	0.269517	−	0.962996i	$-0.413136\pi$
$457$	26.4708	−	15.2830i	1.23825	−	0.714906i	0.968737	+	0.248089i	$0.0798027\pi$
$458$		0			0
$459$	1.79335	−	3.10617i	0.0837063	−	0.144984i
$460$		0			0
$461$	4.05146	+	2.33911i	0.188695	+	0.108943i	0.591372	−	0.806399i	$-0.298587\pi$
$461$	4.05146	+	2.33911i	0.188695	+	0.108943i	−0.402676	+	0.915342i	$0.631920\pi$
$462$		0			0
$463$			14.0011i			0.650688i	0.945596	+	0.325344i	$0.105480\pi$
$463$			14.0011i			0.650688i	−0.945596	+	0.325344i	$0.894520\pi$
$464$		0			0
$465$	−2.06939	−	3.58429i	−0.0959656	−	0.166217i
$466$		0			0
$467$	−6.98506			−0.323230			−0.161615	−	0.986854i	$-0.551670\pi$
$467$	−6.98506			−0.323230			−0.161615	+	0.986854i	$0.551670\pi$
$468$		0			0
$469$	15.4223			0.712135
$470$		0			0
$471$	−3.42371	−	5.93004i	−0.157756	−	0.273242i
$472$		0			0
$473$		−	0.681482i		−	0.0313346i
$474$		0			0
$475$	4.96410	+	2.86603i	0.227769	+	0.131502i
$476$		0			0
$477$	17.4461	−	30.2176i	0.798804	−	1.38357i
$478$		0			0
$479$	14.1065	−	8.14438i	0.644542	−	0.372126i	−0.141820	−	0.989892i	$-0.545296\pi$
$479$	14.1065	−	8.14438i	0.644542	−	0.372126i	0.786362	+	0.617766i	$0.211962\pi$
$480$		0			0
$481$	−0.339423	−	2.70985i	−0.0154764	−	0.123558i
$482$		0			0
$483$	−17.8071	+	10.2810i	−0.810253	+	0.467800i
$484$		0			0
$485$	2.11078	−	3.65597i	0.0958454	−	0.166009i
$486$		0			0
$487$	−17.3559	−	10.0204i	−0.786471	−	0.454069i	0.0522474	−	0.998634i	$-0.483362\pi$
$487$	−17.3559	−	10.0204i	−0.786471	−	0.454069i	−0.838719	+	0.544565i	$0.816695\pi$
$488$		0			0
$489$		−	45.1810i		−	2.04316i
$490$		0			0
$491$	7.89916	+	13.6818i	0.356484	+	0.617449i	0.987371	−	0.158426i	$-0.0506420\pi$
$491$	7.89916	+	13.6818i	0.356484	+	0.617449i	−0.630887	+	0.775875i	$0.717309\pi$
$492$		0			0
$493$	−6.02540			−0.271370
$494$		0			0
$495$	5.33734			0.239896
$496$		0			0
$497$	−9.30208	−	16.1117i	−0.417255	−	0.722708i
$498$		0			0
$499$			1.24651i			0.0558016i	0.999611	+	0.0279008i	$0.00888226\pi$
$499$			1.24651i			0.0558016i	−0.999611	+	0.0279008i	$0.991118\pi$
$500$		0			0
$501$	−35.2361	−	20.3436i	−1.57423	−	0.908883i
$502$		0			0
$503$	−3.82672	+	6.62808i	−0.170625	+	0.295532i	−0.938639	−	0.344902i	$-0.887912\pi$
$503$	−3.82672	+	6.62808i	−0.170625	+	0.295532i	0.768013	+	0.640434i	$0.221245\pi$
$504$		0			0
$505$	13.2048	−	7.62379i	0.587605	−	0.339254i
$506$		0			0
$507$	−9.95732	+	35.3742i	−0.442220	+	1.57102i
$508$		0			0
$509$	−22.2777	+	12.8621i	−0.987444	+	0.570101i	−0.904509	−	0.426454i	$-0.859763\pi$
$509$	−22.2777	+	12.8621i	−0.987444	+	0.570101i	−0.0829345	+	0.996555i	$0.526429\pi$
$510$		0			0
$511$	3.54035	−	6.13207i	0.156616	−	0.271267i
$512$		0			0
$513$	−27.9393	−	16.1308i	−1.23355	−	0.712192i
$514$		0			0
$515$		−	13.5269i		−	0.596067i
$516$		0			0
$517$	−5.05080	−	8.74824i	−0.222134	−	0.384747i
$518$		0			0
$519$	68.8305			3.02132
$520$		0			0
$521$	−30.1519			−1.32098			−0.660490	−	0.750835i	$-0.729651\pi$
$521$	−30.1519			−1.32098			−0.660490	+	0.750835i	$0.729651\pi$
$522$		0			0
$523$	1.96876	+	3.41000i	0.0860880	+	0.149109i	0.905854	−	0.423589i	$-0.139230\pi$
$523$	1.96876	+	3.41000i	0.0860880	+	0.149109i	−0.819766	+	0.572698i	$0.805897\pi$
$524$		0			0
$525$			5.38573i			0.235052i
$526$		0			0
$527$	−0.808017	−	0.466509i	−0.0351978	−	0.0203215i
$528$		0			0
$529$	4.21200	−	7.29539i	0.183130	−	0.317191i
$530$		0			0
$531$	−3.20301	+	1.84926i	−0.138999	+	0.0802510i
$532$		0			0
$533$	0.120072	+	0.958614i	0.00520088	+	0.0415222i
$534$		0			0
$535$	6.37632	−	3.68137i	0.275672	−	0.159159i
$536$		0			0
$537$	−5.35444	+	9.27415i	−0.231061	+	0.400209i
$538$		0			0
$539$	3.12117	+	1.80201i	0.134438	+	0.0776180i
$540$		0			0
$541$		−	15.8881i		−	0.683083i	−0.939867	−	0.341541i	$-0.889051\pi$
$541$		−	15.8881i		−	0.683083i	0.939867	−	0.341541i	$-0.110949\pi$
$542$		0			0
$543$	−11.9970	−	20.7795i	−0.514842	−	0.891732i
$544$		0			0
$545$	10.0760			0.431607
$546$		0			0
$547$	6.56107			0.280531			0.140266	−	0.990114i	$-0.455204\pi$
$547$	6.56107			0.280531			0.140266	+	0.990114i	$0.455204\pi$
$548$		0			0
$549$	−10.4775	−	18.1476i	−0.447170	−	0.774522i
$550$		0			0
$551$			54.1972i			2.30888i
$552$		0			0
$553$	15.3766	+	8.87769i	0.653880	+	0.377518i
$554$		0			0
$555$	1.07059	−	1.85432i	0.0454441	−	0.0787116i
$556$		0			0
$557$	6.79835	−	3.92503i	0.288055	−	0.166309i	−0.349009	−	0.937119i	$-0.613482\pi$
$557$	6.79835	−	3.92503i	0.288055	−	0.166309i	0.637065	+	0.770810i	$0.280148\pi$
$558$		0			0
$559$	1.38724	+	1.83164i	0.0586741	+	0.0774702i
$560$		0			0
$561$	1.66835	−	0.963220i	0.0704377	−	0.0406672i
$562$		0			0
$563$	7.77976	−	13.4749i	0.327878	−	0.567901i	−0.654213	−	0.756310i	$-0.727000\pi$
$563$	7.77976	−	13.4749i	0.327878	−	0.567901i	0.982091	+	0.188410i	$0.0603333\pi$
$564$		0			0
$565$	5.79203	+	3.34403i	0.243673	+	0.140684i
$566$		0			0
$567$		−	1.78554i		−	0.0749857i
$568$		0			0
$569$	1.73957	+	3.01303i	0.0729267	+	0.126313i	0.900183	−	0.435512i	$-0.143433\pi$
$569$	1.73957	+	3.01303i	0.0729267	+	0.126313i	−0.827256	+	0.561825i	$0.810099\pi$
$570$		0			0
$571$	−21.5118			−0.900240			−0.450120	−	0.892968i	$-0.648619\pi$
$571$	−21.5118			−0.900240			−0.450120	+	0.892968i	$0.648619\pi$
$572$		0			0
$573$	15.3868			0.642791
$574$		0			0
$575$	1.90893	+	3.30636i	0.0796078	+	0.137885i
$576$		0			0
$577$		−	9.97608i		−	0.415310i	−0.978202	−	0.207655i	$-0.933417\pi$
$577$		−	9.97608i		−	0.415310i	0.978202	−	0.207655i	$-0.0665831\pi$
$578$		0			0
$579$	−29.7632	−	17.1838i	−1.23692	−	0.714134i
$580$		0			0
$581$	−4.87523	+	8.44414i	−0.202259	+	0.350322i
$582$		0			0
$583$	6.47451	−	3.73806i	0.268147	−	0.154815i
$584$		0			0
$585$	−14.3453	+	10.8648i	−0.593107	+	0.449205i
$586$		0			0
$587$	−20.8341	+	12.0286i	−0.859915	+	0.496472i	−0.863984	−	0.503519i	$-0.832038\pi$
$587$	−20.8341	+	12.0286i	−0.859915	+	0.496472i	0.00406862	+	0.999992i	$0.498705\pi$
$588$		0			0
$589$	−4.19615	+	7.26795i	−0.172899	+	0.299471i
$590$		0			0
$591$	−10.7186	−	6.18837i	−0.440903	−	0.254556i
$592$		0			0
$593$			0.940219i			0.0386102i	0.999814	+	0.0193051i	$0.00614538\pi$
$593$			0.940219i			0.0386102i	−0.999814	+	0.0193051i	$0.993855\pi$
$594$		0			0
$595$	0.607061	+	1.05146i	0.0248871	+	0.0431057i
$596$		0			0
$597$	58.9037			2.41077
$598$		0			0
$599$	11.4270			0.466896			0.233448	−	0.972369i	$-0.424999\pi$
$599$	11.4270			0.466896			0.233448	+	0.972369i	$0.424999\pi$
$600$		0			0
$601$	18.0215	+	31.2142i	0.735114	+	1.27325i	0.954674	+	0.297655i	$0.0962045\pi$
$601$	18.0215	+	31.2142i	0.735114	+	1.27325i	−0.219560	+	0.975599i	$0.570462\pi$
$602$		0			0
$603$			40.4012i			1.64526i
$604$		0			0
$605$	−8.53590	−	4.92820i	−0.347034	−	0.200360i
$606$		0			0
$607$	19.9454	−	34.5464i	0.809557	−	1.40219i	−0.103614	−	0.994618i	$-0.533041\pi$
$607$	19.9454	−	34.5464i	0.809557	−	1.40219i	0.913171	−	0.407576i	$-0.133626\pi$
$608$		0			0
$609$	−44.1003	+	25.4613i	−1.78704	+	1.03175i
$610$		0			0
$611$	31.3833	+	13.2314i	1.26963	+	0.535285i
$612$		0			0
$613$	0.299187	−	0.172736i	0.0120841	−	0.00697673i	−0.493946	−	0.869493i	$-0.664446\pi$
$613$	0.299187	−	0.172736i	0.0120841	−	0.00697673i	0.506030	+	0.862516i	$0.331113\pi$
$614$		0			0
$615$	−0.378725	+	0.655970i	−0.0152716	+	0.0264513i
$616$		0			0
$617$	33.5022	+	19.3425i	1.34875	+	0.778700i	0.988072	−	0.153991i	$-0.0492128\pi$
$617$	33.5022	+	19.3425i	1.34875	+	0.778700i	0.360676	+	0.932691i	$0.382546\pi$
$618$		0			0
$619$		−	14.8971i		−	0.598764i	−0.954133	−	0.299382i	$-0.903219\pi$
$619$		−	14.8971i		−	0.598764i	0.954133	−	0.299382i	$-0.0967805\pi$
$620$		0			0
$621$	−10.7440	−	18.6091i	−0.431141	−	0.746758i
$622$		0			0
$623$	−23.9644			−0.960113
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−8.66397	−	15.0064i	−0.346006	−	0.599299i
$628$		0			0
$629$		−	0.482694i		−	0.0192463i
$630$		0			0
$631$	−33.6408	−	19.4225i	−1.33922	−	0.773198i	−0.352526	−	0.935802i	$-0.614677\pi$
$631$	−33.6408	−	19.4225i	−1.33922	−	0.773198i	−0.986691	+	0.162604i	$0.948011\pi$
$632$		0			0
$633$	−15.0581	+	26.0814i	−0.598506	+	1.03664i
$634$		0			0
$635$	1.28994	−	0.744750i	0.0511899	−	0.0295545i
$636$		0			0
$637$	−12.0571	+	1.51022i	−0.477719	+	0.0598370i
$638$		0			0
$639$	42.2072	−	24.3683i	1.66969	−	0.963996i
$640$		0			0
$641$	18.5908	−	32.2003i	0.734293	−	1.27183i	−0.220739	−	0.975333i	$-0.570847\pi$
$641$	18.5908	−	32.2003i	0.734293	−	1.27183i	0.955033	−	0.296501i	$-0.0958197\pi$
$642$		0			0
$643$	−7.88410	−	4.55189i	−0.310918	−	0.179509i	0.336419	−	0.941712i	$-0.390784\pi$
$643$	−7.88410	−	4.55189i	−0.310918	−	0.179509i	−0.647337	+	0.762204i	$0.724118\pi$
$644$		0			0
$645$			1.80144i			0.0709316i
$646$		0			0
$647$	9.56118	+	16.5605i	0.375889	+	0.651059i	0.990460	−	0.137803i	$-0.0440041\pi$
$647$	9.56118	+	16.5605i	0.375889	+	0.651059i	−0.614571	+	0.788862i	$0.710671\pi$
$648$		0			0
$649$	−0.792455			−0.0311066
$650$		0			0
$651$	−7.88525			−0.309047
$652$		0			0
$653$	−17.3162	−	29.9926i	−0.677636	−	1.17370i	−0.975691	−	0.219152i	$-0.929671\pi$
$653$	−17.3162	−	29.9926i	−0.677636	−	1.17370i	0.298055	−	0.954549i	$-0.403662\pi$
$654$		0			0
$655$		−	4.12676i		−	0.161246i
$656$		0			0
$657$	16.0640	+	9.27453i	0.626714	+	0.361834i
$658$		0			0
$659$	−3.34926	+	5.80109i	−0.130469	+	0.225978i	−0.923857	−	0.382737i	$-0.874982\pi$
$659$	−3.34926	+	5.80109i	−0.130469	+	0.225978i	0.793389	+	0.608715i	$0.208315\pi$
$660$		0			0
$661$	5.22004	−	3.01379i	0.203036	−	0.117223i	−0.395035	−	0.918666i	$-0.629268\pi$
$661$	5.22004	−	3.01379i	0.203036	−	0.117223i	0.598071	+	0.801443i	$0.295934\pi$
$662$		0			0
$663$	−2.52331	+	5.98501i	−0.0979974	+	0.232438i
$664$		0			0
$665$	9.45767	−	5.46039i	0.366753	−	0.211745i
$666$		0			0
$667$	−18.0491	+	31.2620i	−0.698865	+	1.21047i
$668$		0			0
$669$	−52.2411	−	30.1614i	−2.01976	−	1.16611i
$670$		0			0
$671$		−	4.48990i		−	0.173330i
$672$		0			0
$673$	11.6784	+	20.2276i	0.450169	+	0.779715i	0.998396	−	0.0566140i	$-0.0180304\pi$
$673$	11.6784	+	20.2276i	0.450169	+	0.779715i	−0.548227	+	0.836329i	$0.684697\pi$
$674$		0			0
$675$	−5.62828			−0.216633
$676$		0			0
$677$	−45.4042			−1.74503			−0.872513	−	0.488590i	$-0.837511\pi$
$677$	−45.4042			−1.74503			−0.872513	+	0.488590i	$0.837511\pi$
$678$		0			0
$679$	−4.02148	−	6.96540i	−0.154330	−	0.267308i
$680$		0			0
$681$			44.3408i			1.69914i
$682$		0			0
$683$	−22.0817	−	12.7489i	−0.844934	−	0.487823i	0.0140045	−	0.999902i	$-0.495542\pi$
$683$	−22.0817	−	12.7489i	−0.844934	−	0.487823i	−0.858938	+	0.512079i	$0.828875\pi$
$684$		0			0
$685$	−10.0548	+	17.4155i	−0.384175	+	0.665411i
$686$		0			0
$687$	−18.6567	+	10.7715i	−0.711798	+	0.410957i
$688$		0			0
$689$	−9.79246	+	23.2266i	−0.373063	+	0.884862i
$690$		0			0
$691$	−5.71257	+	3.29815i	−0.217316	+	0.125468i	−0.604707	−	0.796448i	$-0.706710\pi$
$691$	−5.71257	+	3.29815i	−0.217316	+	0.125468i	0.387391	+	0.921916i	$0.373376\pi$
$692$		0			0
$693$	5.08438	−	8.80641i	0.193140	−	0.334528i
$694$		0			0
$695$	18.0352	+	10.4126i	0.684115	+	0.394974i
$696$		0			0
$697$			0.170754i			0.00646778i
$698$		0			0
$699$	−26.9327	−	46.6487i	−1.01869	−	1.76442i
$700$		0			0
$701$	−29.2474			−1.10466			−0.552329	−	0.833626i	$-0.686261\pi$
$701$	−29.2474			−1.10466			−0.552329	+	0.833626i	$0.686261\pi$
$702$		0			0
$703$	−4.34174			−0.163752
$704$		0			0
$705$	13.3513	+	23.1252i	0.502841	+	0.870946i
$706$		0			0
$707$		−	29.0499i		−	1.09253i
$708$		0			0
$709$	−9.46865	−	5.46673i	−0.355603	−	0.205307i	0.311548	−	0.950231i	$-0.399153\pi$
$709$	−9.46865	−	5.46673i	−0.355603	−	0.205307i	−0.667150	+	0.744923i	$0.732486\pi$
$710$		0			0
$711$	−23.2566	+	40.2815i	−0.872189	+	1.51068i
$712$		0			0
$713$	−4.84084	+	2.79486i	−0.181291	+	0.104668i
$714$		0			0
$715$	−3.82584	+	0.479208i	−0.143078	+	0.0179214i
$716$		0			0
$717$	31.2220	−	18.0260i	1.16601	−	0.673194i
$718$		0			0
$719$	−8.02989	+	13.9082i	−0.299464	+	0.518688i	−0.976014	−	0.217710i	$-0.930141\pi$
$719$	−8.02989	+	13.9082i	−0.299464	+	0.518688i	0.676549	+	0.736398i	$0.263475\pi$
$720$		0			0
$721$	−22.3189	−	12.8858i	−0.831199	−	0.479893i
$722$		0			0
$723$			73.2966i			2.72593i
$724$		0			0
$725$	4.72756	+	8.18837i	0.175577	+	0.304108i
$726$		0			0
$727$	51.3754			1.90541			0.952704	−	0.303900i	$-0.0982889\pi$
$727$	51.3754			1.90541			0.952704	+	0.303900i	$0.0982889\pi$
$728$		0			0
$729$	−43.0532			−1.59456
$730$		0			0
$731$	0.203052	+	0.351697i	0.00751016	+	0.0130080i
$732$		0			0
$733$			9.82358i			0.362842i	0.983406	+	0.181421i	$0.0580697\pi$
$733$			9.82358i			0.362842i	−0.983406	+	0.181421i	$0.941930\pi$
$734$		0			0
$735$	−8.25055	−	4.76346i	−0.304326	−	0.175703i
$736$		0			0
$737$	−4.32824	+	7.49673i	−0.159433	+	0.276146i
$738$		0			0
$739$	−42.5082	+	24.5421i	−1.56369	+	0.902797i	−0.566811	+	0.823848i	$0.691823\pi$
$739$	−42.5082	+	24.5421i	−1.56369	+	0.902797i	−0.996879	+	0.0789487i	$0.974844\pi$
$740$		0			0
$741$	53.8339	+	22.6967i	1.97764	+	0.833783i
$742$		0			0
$743$	35.3663	−	20.4188i	1.29746	−	0.749091i	0.317499	−	0.948259i	$-0.397157\pi$
$743$	35.3663	−	20.4188i	1.29746	−	0.749091i	0.979966	+	0.199167i	$0.0638237\pi$
$744$		0			0
$745$	−6.68388	+	11.5768i	−0.244878	+	0.424142i
$746$		0			0
$747$	−22.1208	−	12.7715i	−0.809358	−	0.467283i
$748$		0			0
$749$		−	14.0276i		−	0.512557i
$750$		0			0
$751$	1.36340	+	2.36148i	0.0497512	+	0.0861716i	0.889829	−	0.456295i	$-0.150824\pi$
$751$	1.36340	+	2.36148i	0.0497512	+	0.0861716i	−0.840077	+	0.542467i	$0.817490\pi$
$752$		0			0
$753$	21.5175			0.784142
$754$		0			0
$755$	18.2984			0.665946
$756$		0			0
$757$	−7.40301	−	12.8224i	−0.269067	−	0.466038i	0.699554	−	0.714580i	$-0.253382\pi$
$757$	−7.40301	−	12.8224i	−0.269067	−	0.466038i	−0.968621	+	0.248542i	$0.920049\pi$
$758$		0			0
$759$		−	11.5413i		−	0.418924i
$760$		0			0
$761$	9.84575	+	5.68445i	0.356908	+	0.206061i	0.667724	−	0.744409i	$-0.267269\pi$
$761$	9.84575	+	5.68445i	0.356908	+	0.206061i	−0.310815	+	0.950470i	$0.600602\pi$
$762$		0			0
$763$	9.59843	−	16.6250i	0.347486	−	0.601864i
$764$		0			0
$765$	−2.75447	+	1.59030i	−0.0995882	+	0.0574972i
$766$		0			0
$767$	2.12991	−	1.61314i	0.0769065	−	0.0582472i
$768$		0			0
$769$	18.2352	−	10.5281i	0.657579	−	0.379654i	−0.133775	−	0.991012i	$-0.542710\pi$
$769$	18.2352	−	10.5281i	0.657579	−	0.379654i	0.791354	+	0.611358i	$0.209377\pi$
$770$		0			0
$771$	0.474602	−	0.822034i	0.0170924	−	0.0296048i
$772$		0			0
$773$	12.1961	+	7.04144i	0.438664	+	0.253263i	0.703031	−	0.711159i	$-0.251830\pi$
$773$	12.1961	+	7.04144i	0.438664	+	0.253263i	−0.264367	+	0.964422i	$0.585163\pi$
$774$		0			0
$775$			1.46410i			0.0525921i
$776$		0			0
$777$	−2.03971	−	3.53288i	−0.0731741	−	0.126741i
$778$		0			0
$779$	1.53590			0.0550293
$780$		0			0
$781$	10.4425			0.373660
$782$		0			0
$783$	−26.6080	−	46.0864i	−0.950893	−	1.64699i
$784$		0			0
$785$			2.42229i			0.0864552i
$786$		0			0
$787$	28.5998	+	16.5121i	1.01947	+	0.588593i	0.913951	−	0.405823i	$-0.133015\pi$
$787$	28.5998	+	16.5121i	1.01947	+	0.588593i	0.105522	+	0.994417i	$0.466349\pi$
$788$		0			0
$789$	−7.59839	+	13.1608i	−0.270510	+	0.468537i
$790$		0			0
$791$	11.0350	−	6.37109i	0.392361	−	0.226530i
$792$		0			0
$793$	9.13974	+	12.0676i	0.324562	+	0.428534i
$794$		0			0
$795$	−17.1148	+	9.88124i	−0.606999	+	0.350451i
$796$		0			0
$797$	−8.47079	+	14.6718i	−0.300051	+	0.519703i	−0.976147	−	0.217110i	$-0.930337\pi$
$797$	−8.47079	+	14.6718i	−0.300051	+	0.519703i	0.676096	+	0.736813i	$0.263670\pi$
$798$		0			0
$799$	5.21319	+	3.00984i	0.184429	+	0.106480i
$800$		0			0
$801$		−	62.7787i		−	2.21817i
$802$		0			0
$803$	1.98719	+	3.44191i	0.0701263	+	0.121462i
$804$		0			0
$805$	7.27382			0.256369
$806$		0			0
$807$	−3.70425			−0.130396
$808$		0			0
$809$	25.8818	+	44.8285i	0.909954	+	1.57609i	0.814125	+	0.580689i	$0.197217\pi$
$809$	25.8818	+	44.8285i	0.909954	+	1.57609i	0.0958292	+	0.995398i	$0.469450\pi$
$810$		0			0
$811$			22.6699i			0.796047i	0.917375	+	0.398023i	$0.130304\pi$
$811$			22.6699i			0.796047i	−0.917375	+	0.398023i	$0.869696\pi$
$812$		0			0
$813$	−28.5091	−	16.4597i	−0.999856	−	0.577267i
$814$		0			0
$815$	−7.99144	+	13.8416i	−0.279928	+	0.484849i
$816$		0			0
$817$	3.16344	−	1.82641i	0.110675	−	0.0638981i
$818$		0			0
$819$	4.26109	+	34.0192i	0.148895	+	1.18873i
$820$		0			0
$821$	−24.8230	+	14.3315i	−0.866328	+	0.500174i	−0.866126	−	0.499826i	$-0.833397\pi$
$821$	−24.8230	+	14.3315i	−0.866328	+	0.500174i	−0.000201482		1.00000i	$0.500064\pi$
$822$		0			0
$823$	12.9164	−	22.3718i	0.450236	−	0.779831i	−0.548165	−	0.836371i	$-0.684673\pi$
$823$	12.9164	−	22.3718i	0.450236	−	0.779831i	0.998400	+	0.0565391i	$0.0180066\pi$
$824$		0			0
$825$	−2.61799	−	1.51150i	−0.0911466	−	0.0526235i
$826$		0			0
$827$			16.0820i			0.559227i	0.960113	+	0.279613i	$0.0902063\pi$
$827$			16.0820i			0.559227i	−0.960113	+	0.279613i	$0.909794\pi$
$828$		0			0
$829$	−11.2909	−	19.5564i	−0.392149	−	0.679222i	0.600584	−	0.799562i	$-0.294935\pi$
$829$	−11.2909	−	19.5564i	−0.392149	−	0.679222i	−0.992733	+	0.120340i	$0.961602\pi$
$830$		0			0
$831$	57.4304			1.99224
$832$		0			0
$833$	−2.14768			−0.0744128
$834$		0			0
$835$	7.19658	+	12.4648i	0.249048	+	0.431364i
$836$		0			0
$837$		−	8.24037i		−	0.284829i
$838$		0			0
$839$	−15.4533	−	8.92198i	−0.533508	−	0.308021i	0.208936	−	0.977929i	$-0.433000\pi$
$839$	−15.4533	−	8.92198i	−0.533508	−	0.308021i	−0.742444	+	0.669908i	$0.766333\pi$
$840$		0			0
$841$	−30.1996	+	52.3073i	−1.04137	+	1.80370i
$842$		0			0
$843$	−29.0698	+	16.7835i	−1.00122	+	0.578053i
$844$		0			0
$845$	9.30735	−	9.07597i	0.320183	−	0.312223i
$846$		0			0
$847$	−16.2627	+	9.38927i	−0.558793	+	0.322619i
$848$		0			0
$849$	32.0169	−	55.4550i	1.09882	−	1.90321i
$850$		0			0
$851$	−2.50440	−	1.44591i	−0.0858497	−	0.0495653i
$852$		0			0
$853$			19.7936i			0.677720i	0.940837	+	0.338860i	$0.110041\pi$
$853$			19.7936i			0.677720i	−0.940837	+	0.338860i	$0.889959\pi$
$854$		0			0
$855$	14.3044	+	24.7759i	0.489199	+	0.847318i
$856$		0			0
$857$	11.7302			0.400696			0.200348	−	0.979725i	$-0.435793\pi$
$857$	11.7302			0.400696			0.200348	+	0.979725i	$0.435793\pi$
$858$		0			0
$859$	−5.37452			−0.183376			−0.0916882	−	0.995788i	$-0.529226\pi$
$859$	−5.37452			−0.183376			−0.0916882	+	0.995788i	$0.529226\pi$
$860$		0			0
$861$	0.721551	+	1.24976i	0.0245904	+	0.0425918i
$862$		0			0
$863$		−	25.3234i		−	0.862017i	−0.902348	−	0.431008i	$-0.858158\pi$
$863$		−	25.3234i		−	0.862017i	0.902348	−	0.431008i	$-0.141842\pi$
$864$		0			0
$865$	−21.0868	−	12.1745i	−0.716973	−	0.413944i
$866$		0			0
$867$	23.4541	−	40.6237i	0.796544	−	1.37965i
$868$		0			0
$869$	−8.63084	+	4.98302i	−0.292781	+	0.169037i
$870$		0			0
$871$	−3.62739	−	28.9599i	−0.122909	−	0.981268i
$872$		0			0
$873$	18.2470	−	10.5349i	0.617567	−	0.356553i
$874$		0			0
$875$	0.952606	−	1.64996i	0.0322040	−	0.0557789i
$876$		0			0
$877$	17.9194	+	10.3458i	0.605095	+	0.349352i	0.771043	−	0.636783i	$-0.219735\pi$
$877$	17.9194	+	10.3458i	0.605095	+	0.349352i	−0.165949	+	0.986134i	$0.553069\pi$
$878$		0			0
$879$			52.6151i			1.77466i
$880$		0			0
$881$	24.1997	+	41.9150i	0.815307	+	1.41215i	0.909107	+	0.416562i	$0.136765\pi$
$881$	24.1997	+	41.9150i	0.815307	+	1.41215i	−0.0937999	+	0.995591i	$0.529901\pi$
$882$		0			0
$883$	45.8550			1.54314			0.771572	−	0.636142i	$-0.219471\pi$
$883$	45.8550			1.54314			0.771572	+	0.636142i	$0.219471\pi$
$884$		0			0
$885$	2.09479			0.0704155
$886$		0			0
$887$	−0.541169	−	0.937332i	−0.0181707	−	0.0314725i	0.856797	−	0.515654i	$-0.172451\pi$
$887$	−0.541169	−	0.937332i	−0.0181707	−	0.0314725i	−0.874968	+	0.484181i	$0.839118\pi$
$888$		0			0
$889$		−	2.83781i		−	0.0951772i
$890$		0			0
$891$	0.867947	+	0.501109i	0.0290773	+	0.0167878i
$892$		0			0
$893$	27.0729	−	46.8916i	0.905959	−	1.56917i
$894$		0			0
$895$	3.28075	−	1.89414i	0.109663	−	0.0633142i
$896$		0			0
$897$	23.4938	+	31.0200i	0.784436	+	1.03573i
$898$		0			0
$899$	−11.9886	+	6.92163i	−0.399842	+	0.230849i
$900$		0			0
$901$	−2.22756	+	3.85824i	−0.0742107	+	0.128537i
$902$		0			0
$903$	2.97231	+	1.71606i	0.0989122	+	0.0571070i
$904$		0			0
$905$			8.48794i			0.282149i
$906$		0			0
$907$	22.7653	+	39.4307i	0.755910	+	1.30928i	0.944920	+	0.327300i	$0.106139\pi$
$907$	22.7653	+	39.4307i	0.755910	+	1.30928i	−0.189010	+	0.981975i	$0.560528\pi$
$908$		0			0
$909$	76.1009			2.52411
$910$		0			0
$911$	−39.7417			−1.31670			−0.658350	−	0.752712i	$-0.728745\pi$
$911$	−39.7417			−1.31670			−0.658350	+	0.752712i	$0.728745\pi$
$912$		0			0
$913$	−2.73645	−	4.73967i	−0.0905632	−	0.156860i
$914$		0			0
$915$			11.8687i			0.392365i
$916$		0			0
$917$	−6.80900	−	3.93118i	−0.224853	−	0.129819i
$918$		0			0
$919$	23.4969	−	40.6978i	0.775091	−	1.34250i	−0.159653	−	0.987173i	$-0.551037\pi$
$919$	23.4969	−	40.6978i	0.775091	−	1.34250i	0.934743	−	0.355323i	$-0.115629\pi$
$920$		0			0
$921$	−7.70608	+	4.44911i	−0.253924	+	0.146603i
$922$		0			0
$923$	−28.0665	+	21.2569i	−0.923821	+	0.699680i
$924$		0			0
$925$	−0.655970	+	0.378725i	−0.0215682	+	0.0124524i
$926$		0			0
$927$	33.7565	−	58.4680i	1.10871	−	1.92034i
$928$		0			0
$929$	−13.1821	−	7.61066i	−0.432489	−	0.249698i	0.267917	−	0.963442i	$-0.413665\pi$
$929$	−13.1821	−	7.61066i	−0.432489	−	0.249698i	−0.700406	+	0.713744i	$0.746998\pi$
$930$		0			0
$931$			19.3180i			0.633121i
$932$		0			0
$933$	4.49551	+	7.78645i	0.147176	+	0.254917i
$934$		0			0
$935$	−0.681482			−0.0222869
$936$		0			0
$937$	6.07285			0.198392			0.0991958	−	0.995068i	$-0.468373\pi$
$937$	6.07285			0.198392			0.0991958	+	0.995068i	$0.468373\pi$
$938$		0			0
$939$	−49.9691	−	86.5490i	−1.63068	−	2.82442i
$940$		0			0
$941$			0.0496576i			0.00161879i	1.00000		0.000809396i	$0.000257639\pi$
$941$			0.0496576i			0.00161879i	−1.00000		0.000809396i	$0.999742\pi$
$942$		0			0
$943$	0.885936	+	0.511495i	0.0288500	+	0.0166566i
$944$		0			0
$945$	−5.36153	+	9.28645i	−0.174411	+	0.302088i
$946$		0			0
$947$	16.1584	−	9.32907i	0.525078	−	0.303154i	−0.213932	−	0.976849i	$-0.568627\pi$
$947$	16.1584	−	9.32907i	0.525078	−	0.303154i	0.739010	+	0.673695i	$0.235294\pi$
$948$		0			0
$949$	−12.3475	−	5.20576i	−0.400816	−	0.168986i
$950$		0			0
$951$	33.3818	−	19.2730i	1.08248	−	0.624969i
$952$		0			0
$953$	−0.764764	+	1.32461i	−0.0247731	+	0.0429083i	−0.878146	−	0.478392i	$-0.841220\pi$
$953$	−0.764764	+	1.32461i	−0.0247731	+	0.0429083i	0.853373	+	0.521301i	$0.174553\pi$
$954$		0			0
$955$	−4.71386	−	2.72155i	−0.152537	−	0.0880673i
$956$		0			0
$957$		−	28.5827i		−	0.923948i
$958$		0			0
$959$	19.1566	+	33.1802i	0.618598	+	1.07144i
$960$		0			0
$961$	28.8564			0.930852
$962$		0			0
$963$	36.7475			1.18417
$964$		0			0
$965$	6.07880	+	10.5288i	0.195683	+	0.338934i
$966$		0			0
$967$			32.1716i			1.03457i	0.855813	+	0.517285i	$0.173057\pi$
$967$			32.1716i			1.03457i	−0.855813	+	0.517285i	$0.826943\pi$
$968$		0			0
$969$	8.94253	+	5.16297i	0.287276	+	0.165859i
$970$		0			0
$971$	−8.62705	+	14.9425i	−0.276855	+	0.479527i	−0.970601	−	0.240692i	$-0.922626\pi$
$971$	−8.62705	+	14.9425i	−0.276855	+	0.479527i	0.693746	+	0.720219i	$0.255959\pi$
$972$		0			0
$973$	34.3609	−	19.8383i	1.10156	−	0.635986i
$974$		0			0
$975$	10.1133	−	1.26675i	0.323884	−	0.0405683i
$976$		0			0
$977$	−13.6164	+	7.86142i	−0.435626	+	0.251509i	−0.701741	−	0.712432i	$-0.747593\pi$
$977$	−13.6164	+	7.86142i	−0.435626	+	0.251509i	0.266114	+	0.963942i	$0.414260\pi$
$978$		0			0
$979$	6.72557	−	11.6490i	0.214950	−	0.372304i
$980$		0			0
$981$	43.5518	+	25.1447i	1.39050	+	0.802807i
$982$		0			0
$983$		−	38.5356i		−	1.22910i	−0.788880	−	0.614548i	$-0.789338\pi$
$983$		−	38.5356i		−	1.22910i	0.788880	−	0.614548i	$-0.210662\pi$
$984$		0			0
$985$	2.18915	+	3.79172i	0.0697521	+	0.120814i
$986$		0			0
$987$	50.8743			1.61935
$988$		0			0
$989$	2.43298			0.0773642
$990$		0			0
$991$	4.29571	+	7.44040i	0.136458	+	0.236352i	0.926153	−	0.377147i	$-0.123095\pi$
$991$	4.29571	+	7.44040i	0.136458	+	0.236352i	−0.789696	+	0.613499i	$0.789762\pi$
$992$		0			0
$993$		−	81.4014i		−	2.58320i
$994$		0			0
$995$	−18.0456	−	10.4186i	−0.572085	−	0.330293i
$996$		0			0
$997$	10.2687	−	17.7859i	0.325213	−	0.563285i	−0.656343	−	0.754463i	$-0.727897\pi$
$997$	10.2687	−	17.7859i	0.325213	−	0.563285i	0.981555	+	0.191178i	$0.0612308\pi$
$998$		0			0
$999$	3.69198	−	2.13157i	0.116809	−	0.0674398i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1040.2.da.b.881.1		8
4.3	odd	2		65.2.m.a.36.1	✓	8
12.11	even	2		585.2.bu.c.361.4		8
13.4	even	6	inner	1040.2.da.b.641.1		8
20.3	even	4		325.2.m.c.49.4		8
20.7	even	4		325.2.m.b.49.1		8
20.19	odd	2		325.2.n.d.101.4		8
52.3	odd	6		845.2.c.g.506.1		8
52.7	even	12		845.2.e.m.191.1		8
52.11	even	12		845.2.a.m.1.4		4
52.15	even	12		845.2.a.l.1.1		4
52.19	even	12		845.2.e.n.191.4		8
52.23	odd	6		845.2.c.g.506.8		8
52.31	even	4		845.2.e.n.146.4		8
52.35	odd	6		845.2.m.g.316.4		8
52.43	odd	6		65.2.m.a.56.1	yes	8
52.47	even	4		845.2.e.m.146.1		8
52.51	odd	2		845.2.m.g.361.4		8
156.11	odd	12		7605.2.a.cf.1.1		4
156.95	even	6		585.2.bu.c.316.4		8
156.119	odd	12		7605.2.a.cj.1.4		4
260.43	even	12		325.2.m.b.199.1		8
260.119	even	12		4225.2.a.bl.1.4		4
260.147	even	12		325.2.m.c.199.4		8
260.199	odd	6		325.2.n.d.251.4		8
260.219	even	12		4225.2.a.bi.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.m.a.36.1	✓	8	4.3	odd	2
65.2.m.a.56.1	yes	8	52.43	odd	6
325.2.m.b.49.1		8	20.7	even	4
325.2.m.b.199.1		8	260.43	even	12
325.2.m.c.49.4		8	20.3	even	4
325.2.m.c.199.4		8	260.147	even	12
325.2.n.d.101.4		8	20.19	odd	2
325.2.n.d.251.4		8	260.199	odd	6
585.2.bu.c.316.4		8	156.95	even	6
585.2.bu.c.361.4		8	12.11	even	2
845.2.a.l.1.1		4	52.15	even	12
845.2.a.m.1.4		4	52.11	even	12
845.2.c.g.506.1		8	52.3	odd	6
845.2.c.g.506.8		8	52.23	odd	6
845.2.e.m.146.1		8	52.47	even	4
845.2.e.m.191.1		8	52.7	even	12
845.2.e.n.146.4		8	52.31	even	4
845.2.e.n.191.4		8	52.19	even	12
845.2.m.g.316.4		8	52.35	odd	6
845.2.m.g.361.4		8	52.51	odd	2
1040.2.da.b.641.1		8	13.4	even	6	inner
1040.2.da.b.881.1		8	1.1	even	1	trivial
4225.2.a.bi.1.1		4	260.219	even	12
4225.2.a.bl.1.4		4	260.119	even	12
7605.2.a.cf.1.1		4	156.11	odd	12
7605.2.a.cj.1.4		4	156.119	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1040.da (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.41342 - 2.44811i) q^{3} +1.00000i q^{5} +(1.64996 + 0.952606i) q^{7} +(-2.49551 + 4.32235i) q^{9} +O(q^{10})\)	\(q+(-1.41342 - 2.44811i) q^{3} +1.00000i q^{5} +(1.64996 + 0.952606i) q^{7} +(-2.49551 + 4.32235i) q^{9} +(-0.926118 + 0.534695i) q^{11} +(1.40072 - 3.32235i) q^{13} +(2.44811 - 1.41342i) q^{15} +(0.318632 - 0.551886i) q^{17} +(-4.96410 - 2.86603i) q^{19} -5.38573i q^{21} +(-1.90893 - 3.30636i) q^{23} -1.00000 q^{25} +5.62828 q^{27} +(-4.72756 - 8.18837i) q^{29} -1.46410i q^{31} +(2.61799 + 1.51150i) q^{33} +(-0.952606 + 1.64996i) q^{35} +(0.655970 - 0.378725i) q^{37} +(-10.1133 + 1.26675i) q^{39} +(-0.232051 + 0.133975i) q^{41} +(-0.318632 + 0.551886i) q^{43} +(-4.32235 - 2.49551i) q^{45} +9.44613i q^{47} +(-1.68508 - 2.91865i) q^{49} -1.80144 q^{51} -6.99102 q^{53} +(-0.534695 - 0.926118i) q^{55} +16.2036i q^{57} +(0.641756 + 0.370518i) q^{59} +(-2.09928 + 3.63606i) q^{61} +(-8.23499 + 4.75447i) q^{63} +(3.32235 + 1.40072i) q^{65} +(7.01029 - 4.04739i) q^{67} +(-5.39623 + 9.34654i) q^{69} +(-8.45663 - 4.88244i) q^{71} -3.71649i q^{73} +(1.41342 + 2.44811i) q^{75} -2.03741 q^{77} +9.31937 q^{79} +(-0.468594 - 0.811629i) q^{81} +5.11778i q^{83} +(0.551886 + 0.318632i) q^{85} +(-13.3640 + 23.1472i) q^{87} +(-10.8932 + 6.28917i) q^{89} +(5.47602 - 4.14741i) q^{91} +(-3.58429 + 2.06939i) q^{93} +(2.86603 - 4.96410i) q^{95} +(-3.65597 - 2.11078i) q^{97} -5.33734i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} + 6 q^{7} - 4 q^{9}+O(q^{10}) \) 8 * q - 2 * q^3 + 6 * q^7 - 4 * q^9	\( 8 q - 2 q^{3} + 6 q^{7} - 4 q^{9} + 6 q^{15} - 2 q^{17} - 12 q^{19} + 10 q^{23} - 8 q^{25} + 4 q^{27} - 8 q^{29} + 42 q^{33} - 10 q^{35} + 6 q^{37} + 12 q^{41} + 2 q^{43} + 12 q^{49} + 8 q^{51} - 24 q^{53} + 12 q^{59} - 28 q^{61} + 24 q^{63} - 8 q^{65} - 6 q^{67} - 16 q^{69} + 2 q^{75} - 36 q^{77} + 16 q^{79} + 8 q^{81} + 18 q^{85} - 22 q^{87} + 24 q^{89} - 28 q^{91} + 16 q^{95} - 30 q^{97}+O(q^{100}) \) 8 * q - 2 * q^3 + 6 * q^7 - 4 * q^9 + 6 * q^15 - 2 * q^17 - 12 * q^19 + 10 * q^23 - 8 * q^25 + 4 * q^27 - 8 * q^29 + 42 * q^33 - 10 * q^35 + 6 * q^37 + 12 * q^41 + 2 * q^43 + 12 * q^49 + 8 * q^51 - 24 * q^53 + 12 * q^59 - 28 * q^61 + 24 * q^63 - 8 * q^65 - 6 * q^67 - 16 * q^69 + 2 * q^75 - 36 * q^77 + 16 * q^79 + 8 * q^81 + 18 * q^85 - 22 * q^87 + 24 * q^89 - 28 * q^91 + 16 * q^95 - 30 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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